Alex's Cycle Blog

Monday, August 26, 2013

In February I posted an item, The sum of the parts, which discussed the energy demands of cycling, and explored the age old "wheel weight versus wheel aerodynamics" debate, and gave some examples of wheel choice by way of modelling the weight vs aero performance trade offs using a forward integration model to consider dynamic acceleration scenarios.

I'm going to return to dynamic modelling one day to explore more realistic acceleration power outputs than the constant power examples used, but not today. Modelling a dynamically changing scenario is a bit trickier than steady state (constant velocity) scenario, and it's the latter I'm posting about today, more for the record than anything else in particular. Hey, I was asked, so here goes.

Relative energy demand for steady state road cycling

In the introduction to that item was the chart below, which shows the relative energy demand for steady state cycling for each of the main resistance forces, for gradients ranging from flat (0%) to steep (10%). The idea being to show how the relative importantance of each resistance force varies with zero or positive gradients. The assumptions used are listed in the table on the chart. Click on the chart to see a larger version.

I didn't include negative gradients (descending), as the charting starts gets a little funky - since gravity in that scenario is aiding our forward motion, rather than resisting it. Suffice to say that air resistance is still dominant when going downhill. Besides we tend not to put out nearly as much power going downhills, and brakes also come into play depending on the terrain.

So back to non-negative gradient chit chat.

We can see how air resistance is the dominant resistance force on flatter terrain and hence why aerodynamics matters a lot on flatter and shallower gradients, gradually giving way to gravity which dominates as the climb becomes steeper and our speed slows. This is why weight is an important performance factor on the slopes but much less so on flat ground.

The assumptions used to generate the chart were for a road cyclist in a fairly aerodynamic road bike position, although one would expect them to ride in a less aerodynamic position as the slope steepens. These minor assumption variations don't really change the overall chart trend much.

How about for MTB?

If we change the input assumptions (e.g. CdA, rider mass) all that will happen is the overall trends will shift a bit to the left or right, so having those assumptions precisely right isn't really the point of the chart, it's more about how the components of proportional energy demand vary by gradient.

As an example of modifying those assumptions, a while back for Mountain Bike Magazine, to assist with an article discussing the relative merits of 26" and 19" wheels (see those wheel arguments happen everywhere!), I created the same chart shown below but used alternative input assumptions more akin to MTB riding.

We can see that the same pattern appears as for the road cyclist, however the relative importance of the various forces is somewhat different, and in particular note the larger relative energy demand of rolling resistance due to MTB tyres and rougher terrain. Still, aero still matters in MTB on the shallower terrain, and is something to consider with bike set up depending on the type of racing you do and course profile.

Of course cycle racing is not just about the physics of the energy demand factors or the physiology of energy supply (power output). Skill, experience, strategy, tactics, technical factors and psychology all play their part. This was simply to demonstrate the relative importance of the key physical factors involved.

Get more aero, get lighter, get quality tyres and get fitter. Simple really.

6
comments:

Nice! I wonder how good the Crr model of rolling resistance is on a mountain bike The principal assumptions are (1) resistance is proportional to weight (2) resistance is proportional to speed. With a bike rattling over rough trails it's easy to imagine that neither of these assumptions is good, although averaged over a large population of trails, perhaps the model does as well as any other.

"Rolling resistance" in a road bike is typically modeled as primarily due to deformation of the tire. On a mountain bike it is likely more related to vibrations. This, perhaps, complicates matters.

@djconnelYes, the context for the MTB magazine was for fairly hard pack trails. Clearly loose and/or rough terrain brings with it all sorts of other variables, and presumably a loss of drivetrain efficiency as well.

Really it was just to illustrate how the relative forces vary in different situations (and for me to simply publish a chart I'd done a whie back).

I've no real idea how one would or could reconfigure the Crr model for such terrain. Maybe it's more a drivetrain efficiency thing, with losses between tyre and surface.

I'm not really sure what additional value extending the charts adds. The gravity portion of the energy demand will just gradually increase from the 85% mark closer to 90+% of total energy demand. IOW at steep gradients the energy is almost wholly due to overcoming gravity, all that happens is the speed slows the steeper it gets.

For riders of different weights, the chart looks exactly the same shape, just the gravity portion of energy demand is a bit more at each gradient for heavier riders, and a bit less for lighter riders. Or if you like, it'd be like shifting the gradient values for each column to the left or right.

Knowing the precise values wasn't really the point of the exercise, rather it is simply to show the relative importance of each of the energy demand factors when riding on terrain of different gradients.

As for downhills, yes of course you get a return of gravitational potential energy, which is why you can coast at speed for zero power input. Pedalling at a given power on a descent simply increases speed attainable, or the rate at which you accelerate.